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A116715
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Number of permutations of length n which avoid the patterns 312, 2341, 4321.
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2
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1, 2, 5, 12, 25, 54, 120, 265, 580, 1272, 2796, 6143, 13488, 29619, 65053, 142873, 313771, 689095, 1513390, 3323699, 7299465, 16031000, 35207128, 77321545, 169812767, 372941033, 819049274, 1798787604, 3950478790, 8676000808, 19054143661, 41846514135
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1 + x)*(1 + 2*x^2 + x^3) / (1 - x - x^2 - 2*x^3 - 3*x^4 - x^5).
a(n) = a(n-1) + a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5) for n>5. - Colin Barker, Oct 20 2017
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PROG
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(PARI) Vec(x*(1 + x)*(1 + 2*x^2 + x^3) / (1 - x - x^2 - 2*x^3 - 3*x^4 - x^5) + O(x^40)) \\ Colin Barker, Oct 20 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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